Global well-posedness and limit behavior for the modified finite-depth-fluid equation

Details Global well-posedness and limit behavior for the modified finite-depth-fluid equation Global well-posedness and limit behavior for the modified finite-depth-fluid equation

2008-09-13

arxiv.org/abs/0809.2318v1

Mathematics

Analysis of PDEs

29 pages, 0 figures

Scientific paper

Considering the Cauchy problem for the modified finite-depth-fluid equation $\partial_tu-\G_\delta(\partial_x^2u)\mp u^2u_x=0, u(0)=u_0$, where $\G_\delta f=-i \ft ^{-1}[\coth(2\pi \delta \xi)-\frac{1}{2\pi \delta \xi}]\ft f$, $\delta\ges 1$, and $u$ is a real-valued function, we show that it is uniformly globally well-posed if $u_0 \in H^s (s\geq 1/2)$ with $\norm{u_0}_{L^2}$ sufficiently small for all $\delta \ges 1$. Our result is sharp in the sense that the solution map fails to be $C^3$ in $H^s (s<1/2)$. Moreover, we prove that for any $T>0$, its solution converges in $C([0,T]; H^s)$ to that of the modified Benjamin-Ono equation if $\delta$ tends to $+\infty$.

Affiliated with

Also associated with

No associations

Rating

Global well-posedness and limit behavior for the modified finite-depth-fluid equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Global well-posedness and limit behavior for the modified finite-depth-fluid equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Global well-posedness and limit behavior for the modified finite-depth-fluid equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-603782